As the popularity of three dimensional video, security of stereo image has become an evident issue to be solved. This paper presents a disparity based stereo image reversible data hiding by using histogram shifting, which can recover the original stereo image from marked stereo image without any distortion. Inter-correlations between left and right views of stereo image are utilized to predict pixels accurately. Then prediction error bins are constructed, and many points are around zero-valued bin for embedding data with low distortion of stereo images. The zero-valued bin is used twice to embed data, so that embedding capacity can reach more than 1 bit per pixel. Experimental results demonstrate that the proposed method outperforms the extended stereo image data hiding methods.